When Z cut Tenchi nothing happened, he just floated there in shock. Ryoko grabbed onto him, and then he used his powers to defeat Z, only then was he sent to the hyperdimension (because he consciously used and lost control of his powers). Stop lying.
The Two Worlds from Parallel Dual were parallel universes. This is constantly stated throughout the show. They each had their own versions of earth, stars, different characters, etc. They split when Kazuki's father discovered the artifact (in one universe he kept it, in the other he threw it away). Anyone can see this.
Are you honestly arguing that there were two planets in the same universe that were both identical to Earth, down to their history, position in space, evolution of life, and even had alternate versions of the same characters?
Zinv's 2 LHWs merged the two universes together. Z's 2 LHWs required power that would shatter the third dimension to defeat. Z's 2 LHWs easily survived Tsunami and Tokimi's galaxy devastation. Z blocked Ryo-Ohki's attack with 1 LHW, and Ryo-Ohki > Chobimaru (stated in GXP). Tenchi's 3 LHWs resisted the infinite force and gravity beyond the event horizon of a black hole. Tenchi's LHWs blocked the Chobimaru's blast completely, it never even hit him, and was stopped in its tracks. The activation of his powers which he was not used to (the strain of summoning 6 LHWs) sent him to the hyperdimension.